Economic growth on the whole is exponential, that's why it's expressed as percentage growth.
The rest of technology looks like many separate curves, which do tend to show exponential or logistic shapes, at least for long periods, from agriculture yields to coal plant efficiency, to solar. Economies do that too: the norm is exponential growth, n% multiplicative increase per year, rather than linear growth. There are shifts, e.g. the fast exponential for top speeds in aerospace ended once we got into space, while DNA sequencing just increased its growth rate several fold, but it's common for annual change to be multiplicative rather than additive.
Check out the Performance Curve Database for many individual improvement curves.
I spent about 50 hours researching technological forecasting methods in the past few months and the performance curves database does look to be the most exciting thing happening in that field.
Ray Kurzweil's writings are the best-known expression of Singularity memes, so I figured it's about time I read his 2005 best-seller The Singularity is Near.
Though earlier users of the term "technological Singularity" used it to refer to the arrival of machine superintelligence (an event beyond which our ability to predict the future breaks down), Kurzweil's Singularity is more vaguely defined:
Kurzweil says that people don't expect the Singularity because they don't realize that technological progress is largely exponential, not linear:
Kurzweil has many examples:
He emphasizes that people often fail to account for how progress in one field will feed on accelerating progress in another:
Kurzweil's second chapter aims to convince us that Moore's law of exponential growth in computing power is not an anomaly: the "law of accelerating returns" holds for a wide variety of technologies, evolutionary developments, and paradigm shifts. The chapter is full of logarithmic plots for bits of DRAM per dollar, microprocessor clock speed, processor performance in MIPS, growth in Genbank, hard drive bits per dollar, internet hosts, nanotech science citations, and more.
The chapter is a wake-up call to those not used to thinking about exponential change, but one gets the sense that Kurzweil has cherry-picked his examples. Plenty of technologies have violated his law of accelerating returns, and Kurzweil doesn't mention them.
This cherry-picking is one of the two persistent problems with The Singularity is Near. The second persistent problem is detailed storytelling. Kurzweil would make fewer false predictions if he made statements about the kinds of changes we can expect and then gave examples as illustrations, instead of giving detailed stories about the future as his actual predictions.
My third major issue with the book is not a "problem" so much as it is a decision about the scope of the book. Human factors (sociology, psychology, politics) are largely ignored in the book , but would have been illuminating to include if done well — and certainly, they are important for technological forecasting.
It's a big book with many specific claims, so there are hundreds of detailed criticisms I could make (e.g. about his handling of AI risks), but I prefer to keep this short. Kurzweil's vision of the future is more similar to what I expect is correct than most people's pictures of the future are, and he should be applauded for finding a way to bring transhumanist ideas to the mainstream culture.